Why Does Glass Break?

US-China Winter SchoolNew Functionalities in Glass

Why Does Glass Break?Some considerations of the mechanical

properties of glass

Richard K. Brow

Missouri University of Science & Technology

Department of Materials Science & Engineering

2010 US-ChinaWinter School

Richard K. [email protected]

IMI-1

If glass was 100X stronger, what *new* applications would result?


IMI-22010 US-ChinaWinter School

New applications will benefit from stronger glass…..



Apple Store, 5th Ave., NYC Glasgow, Scotland



Train Station/Strasbourg, France



Emilio Spinosa, O-I, Vancouver, June 2009



Strong glass comes in handy for other applications



Our Outline

1. Background Information• Elastic modulus• Fracture mechanics and strength• Fatigue• Strengthening

2. Two-point bend studies of pristine glass



Some useful references:

• A. Varshneya, “Fundamentals of Inorganic Glasses”, Society of Glass Technology (2006)- chap. 18

• “Elastic Properties and Short-to Medium-Range Order in Glasses”, Tanguy Rouxel, J. Am. Ceram. Soc., 90 [10] 3019–3039 (2007)

• “Environmentally Enhanced Fracture of Glass: A Historical Perspective,” S. W. Frieman, S.M. Weiderhorn, and J.J. Mecholsky, J. Am. Ceram. Soc. 92[7] 1371-1382 (2009)

• M. Ciccotti, “Stress-corrosion mechanisms in silicate glasses,” J. Phys. D: Appl. Phys. 42, 214006 (2009).

• C. R. Kurkjian, P. K. Gupta, R. K. Brow, and N. Lower,” The intrinsic strength and fatigue of oxide glasses’, J. Noncryst. Solids, 316, 114 (2003).





Can we connect mechanical performance to the molecular structure of glass?

E

U

r

r0

U0

Elastic Modulus

Definitions?Why should we care about modulus?



Elastic Modulus- resistance to deflection

xx

E

Why is the elastic modulus of a glass important?• Stiffer hard-drive disks (minimize deflection at high

rpm’s)• Stiffer glass-fiber reinforces composites (larger wind-

turbine blades)• Reduce the thickness (and weight) of architectural

glass)• Increase the stiffness of glass-bearing structures

(buildings, bio-glass scaffolds, etc.)• Design glass or glass-ceramic matrices

for aerospace applications

x

y, z

Poisson‟s Ratio



Elastic Modulus Is Related To The Strength of Nearest Neighbor Bonds

U

r

Force = F = - dU/dr

Stiffness = S0 = (dU2/dr2) r = r0

Elastic Modulus = E = S / r0

r0F

rr0

Elastic Modulus: Pascals = J/m3

a measure of the volume density

of strain energy (E≈U0/V0)

U0

0

0

2

2

0

90

UV

mn

V

UVK

V

Bulk Modulus:



0

0

2

2

0

90

UV

mn

V

UVK

V

From atomistic to continuum properties:

Multi-component glasses:

)()()(

//

000

0

0

yxfffai

iiiaii

BAHBHyAHxH

MfHfV

U

i: density

fi: molar fraction of ith component

Mi: molar mass of ith component

Hai: enthalpy of ith component (Born-Haber cycle)



E and Tg are related within a composition class

Rouxel, J. Am. Ceram. Soc., 90 [10] 3019–3039 (2007)



More cross-links:

greater E

Rouxel, J. Am. Ceram. Soc., 90 [10] 3019–3039 (2007)



Poisson‟s ratio appears to be sensitive to structure: packing

density and „network dimensionality‟




IMI-182010 US-ChinaWinter SchoolRouxel, J. Am. Ceram. Soc., 90 [10] 3019–3039 (2007)

2010 IMIRichard K. [email protected]

IMI-19Rouxel, J. Am. Ceram. Soc., 90 [10] 3019–3039 (2007)

The temperature-dependence of the Poisson‟s ratio may

indicate changes in structure through the glass transition

2010 IMIRichard K. [email protected]

IMI-20Rouxel, J. Am. Ceram. Soc., 90 [10] 3019–3039 (2007)

Summary: Elasticity

•There is a limited correlation between E and Tg within

compositional series, but not necessarily between

compositional types

•High elastic moduli are favored by structural disorder and

atomic packing seems to be more important than bond

strength

•Poisson‟s ratio ( ) correlates with atomic packing density

and with network dimensionality (polymerization)

•The temperature dependence of elastic properties above

Tg may be related to “fragile” and “strong” viscosity

behavior.



Glass Strength


IMI-22

What factors determine the strength of glass?


Theoretical Strength Can Be Estimated From the Potential Energy Curve (Orowan)

2 f = m sin( x/ ) dx

= m / ( )

a0

m = E / a0

m = [ f E / a0 ]1/2

If E = 70 GPa, f = 3.5 J/m2

and a0 = 0.2nm, then

m = 35 GPa !



How does the addition of Na2O affect the Young’s modulus and fracture surface energy of silica glass? Consider what Prof. Pantano discussed the other day….



Practical strengths are significantly less than

the theoretical strengths:

Common glass products 14-70 MPa

Freshly drawn glass rods 70-140 MPa

Abraded glass rods 14-35 MPa

Wet, scored glass rods 3-7 MPa

Armored glass 350-500 MPa

Handled glass fibers 350-700 MPa

Freshly drawn glass fibers 700-2100 MPa

Most metals, including steels 140-350 MPa



C. E. Inglis (1913): flaws acted as stress concentratorsA.A Griffith (1921): critical flaws determine strength

Stress enhancement by flaws

with length 2c and radius :

yy ≈ 2 a (c/ )1/2


IMI-26

Calculated strength with

critical flaw c*:

f = [2 f E / c*] 1/2

If E = 70 GPa, and f = 3.5 J/m2

Then a crack of 100 microns will

result in a failure stress of ≈ 25 MPa


Fracture mechanics allow the evaluation of stresses in

the vicinity of a propagating crack

ij = [K / (2 r)1/2] fij ( )

KIc = a ( c)1/2

Fracture criterion when

stress intensity exceeds

the strain energy release rate (depends on E, f)



Cathodoluminescence measurements of stress distributions around crack tips

(Pezzotti and Leto, 2007)



P, p

rob

ab

ility

de

nsity

, applied stress

m

d

, applied stressPF, cum

ula

tive failu

re p

rob.

1.0

m2

m1

Note: same „average‟

fracture strength, but

m1<m2 (broader distri-

bution of strengths).

ln

lnln

(1-P

F)-

1

m

An aside: Weibull Statistics

2

2

2

)(exp

2

1

dd

Pm

m

FP

0

exp1

0lnln1lnln mP

F



Smith and Michalske, 1992

Room temperature tensile tests of pristine silica fibers

drawn and tested in vacuum- bimodal distribution

14GPa

9GPa




IMI-31

The Ultimate Strength of Glass Silica Nanowires, G. Brambilla and DN Payne, Nano

Letters, 9[2] 831 (2009)

Flame-attenuation of optical fibers

Fiber diameter (nm)

Failu

re s

trength

(G

Pa)


E-glass fibers (tensile tests, in air)

Lower soak temperatures

lead to bimodal strength

distributions

Cameron, 1968



Gulati, et al., Ceramic Bulletin,

83[5] 14, 2004

Concentric ring tests,

abraded Corning glass 1737,

two different thicknesses.



Baikova, et al. Glass Phys. Chem., 21[2] (1995) 115.

E

Hv

LN

RT

K/Al-metaphosphate glasses

Mechanical properties depend on glass structure



Pukh et al., 2005



MD Simulations of fracture

reveal the development of

cavities that coalesce to

form the failure site

Pedone et al., 2008



Quenched and annealed soda-lime glasses at 5GPa tension

S. Ito and T. Taniguchi, JNCS (2004)



There may be experimental evidence for cavitation near

the tips of slow-moving cracks

Aluminosilicate glass, 10-11 m/s, 45% RH, AFM Images

Formation of „nano-cavities‟ interpreted as evidence for „nano-

ductile‟ fracture of glass!



Célarié, et al., PRL (2003)

„Nano-ductility‟ interpretation is not universal

„Post-mortem‟ AFM

analyses of the opposing

fracture surfaces show no

evidence for the formation

of nano-cavities

Guin and Wiederhorn, PRL (2004)

Note the relatively rough surface



Fatigue



http://www.youtube.com/watch?v=r8q-R9ZISac


IMI-41

An example of fatigue in glass





F la w S iz e (m )

1 e -9 1 e -8 1 e -7 1 e -6 1 e -5 1 e -4

Fa

ilu

re S

tre

ng

th (

MP

a)

1

1 0

1 0 0

1 0 0 0

1 0 0 0 0

In h e re n t

F la w s

S tru c tu ra l

F la w s

F a b r i-

c a t io n

-s c o p ic

D a m a g e

V is ib le

D a m a g e

P r is t in e , A s -D ra w n

P r is t in e , A n n e a le d

F o rm e d G la s s

U s e d G la s s

D a m a g e d

G la s s

S ta t icF a t ig u e

E ffe c t

In s ta n ta n e o u s S tre n g thE n d u ra n c e L imit

After Mould (1967)



Stress Corrosion: source for static fatigue- the

reduction in strength with time



Fatigue data on silica fibers

Room temperature, ambient conditions

Room temperature, vacuum

Liquid nitrogen



Note: residual

stresses increase

susceptibility to

static fatigue



V=dc/dt

K=P2/f(geometry)

S. W. Freiman, D. R. Mulville and P. W. Mast, J. Mater. Sci., 8[11] 1573 (1973).

c

Double-Cantilever Beam

(DCB) used for controlled

stress intensity and crack

velocity experiments



Region I: stress-corrosion

Region II: diffusion-limited

Region III: rapid fracture (KIC)

Region 0: propagation threshold



Crack propagation kinetics depend on the stress intensity


IMI-49

SM Wiederhorn, JACerS, 50 407 (1967)

Cra

ck v

elo

city (

m/s

)

Stress Intensity Factor, KI (Nm-1/2)

H2O(l)

I

II

III

100%

30%

10%

1.0%

0.2%

0.017%

Water and stress enhance crack growth in glass

Region I: stress-

corrosion

v=AKIn, where n is the

„stress corrosion

susceptibility factor‟


Compositional-dependence of v-K behavior in Region I

Different glasses are more or less susceptible to fatigue effects –

We do not understand this compositional dependence!


IMI-50

BorosilicateSilica

Soda-Lime

Aluminosilicate


Wiederhorn and Bolz, JACerS, 53, 545 (1970)

Temperature-dependence of v-K behavior in Region I



Slow crack growth is a thermally activated process

)/exp(0

RTbKEVVI

Chemical rate theory has been used to explain the exponential form of the V –KI curves:

where V0 is a constant, E is the activation energy for the reaction, R is the gas constant, T is the temperature, and b is proportional to the activation volume for the crack growth process, ΔV*.

Wiederhorn, et al., JACerS, 1974



Stress-corrosion in silicate glass:

a. Adsorption of a water molecule on a strained siloxane bond at a crack tip;

b. Reaction based on proton and electron transfer;

c. Separation of silanol groups after rupture of the hydrogen bond.

Net result: extension of the crack length by one tetrahedral unit



Stress-corrosion in silicate glass:

a. Reactive molecules can donate both protons and electrons to the ruptured siloxane bond;

b. Reactive molecules are small enough to reach the crack tip (<0.5 nm).

Water, ammonia, hydrazine (H2N-NH2), formamide (CH3NO)



Lawn et al., JACerS, 68[1] 25 (1985)

•Controlled flaws (Vicker’s indents) in S-L-S•Aging in different environments•Tensile tests in inert conditions (silicone oil)•May be due to stress release- not crack geometry?



Other ‘crack-tip chemistries’ lead to strength increasing with time

Change in crack tip geometry due to corrosion: (a) Flaw sharpening for stresses greater than the fatigue limit; (b) Constant flaw sharpness for stresses equal to the fatigue stress; (c) Flaw blunting for stresses below the fatigue limit. .T.-J. Chuang and E.R. Fuller, Jr. “Extended Charles-Hillig Theory for Stress Corrosion Cracking of Glass,” J. Am. Ceram. Soc. 75[3] 540-45 (1992).

W.B. Hillig, “Model of effect of environmental attack on flaw growth kinetics of glass,” Int. J. Fract. 143 219-230 (2007)

Crack-tip sharpness depends on glass structure and corrosion conditions





AFM detects significant morphological changes around the crack-tip in aged samples

• Formation of alkali-rich regions modeled by Na+-H3O+ inter-diffusion• Alkali depletion from crack-tip region leads to stress-relaxation

• Crack extension threshold

SLS glass, 45% RH Célarié, et al., JNCS (2007)

The ‘corrosion reactions’ at a crack tip are similar to those that occur at glass surfaces

From Prof. Jain:

A clear glass plate is made of soda lime silicate glass by pressing molten gob. It shows

the following undesirable pattern upon washing in a dishwasher. Discuss this problem

with your roommate. Then develop a collaborative research program to characterize and

solve the problem. The proposal should be about 1500 words long.





Water plays many roles at a crack-tip

1. Chemical attack on strained bonds to extend flaws

2. Water films adsorbed on crack surfaces

3. Capillary condensation at the crack tip

4. Water diffusion into the glass network, changing elastic properties

5. Inter-diffusion with alkali ions, changing pH and attacking glass

Strengthening- What can we do to make glass stronger (or more reliable)?



• Polished surfaces

• Surface dealkalization

• Protective coatings

• Relaxation of residual stresses (annealing)

• Reduction of expansion coefficients (thermal shock)

• Thermal tempering

• Chemical tempering

• Modified compositions:

– Increasing elastic modulus and/or surface energy

– Reducing stress-corrosion

– Propagation threshold

– Crack healing



Annealed vs. chemically tempered glass

From Jill Glass, Sandia National Labs



Two-point bend studies ofthe failure characteristics of silicate glasses



We have produced and tested pristine fibers

Box Furnace

Drawing Cage

• “Pristine” 10 cm length fibers• Fiber diameters ~125 mm.• Fibers can be tested immediately.

TNL Tool and Technology, LLC – www.TNLTool.com



We have measured failure strains usinga Two-Point Bend technique

• Face plate velocities: 1 – 10,000 mm/sec• Liquid nitrogen, room temp/variable humidity.• Small test volume (25-100mm gauge length). E

dD

d

ff

f

198.1

*M.J. Matthewson, C.R. Kurkjian, S.T.

Gulati, J. Am. Cer. Soc., 69, 815 (1986).

TNL Tool and Technology, LLC – www.TNLTool.com



The inert failure strain measurements are reproducible

F a ilu re S tra in (% )

9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0

Cu

mu

lati

ve

Fa

ilu

re P

rob

ab

ilit

y (

%)

1

3

5

1 0

2 0

4 0

6 0

8 0

9 0

9 9

S ilic a

m = 1 0 3

A v g = 1 7 .9 8 %

E -G la s s

m = 1 1 9

A v g = 1 2 .8 1 %

Eight sets of E-glass

fibers, tested in liquid

nitrogen, collected

over two years



y = -0.00013x + 12.82

12.2

12.4

12.6

12.8

13.0

13.2

70 90 110 130 150 170 190

Fiber diameter ( m)

Fa

ilu

re s

tra

in (

%)

The inert failure strain measurements are intrinsicCriteria for ‘intrinsic’ failure properties*

•Narrow failure distributions: s(failure) < s(fiber diameter)•Failure property (strength, strain) independent of diameter

*Gupta and Kurkjian, JNCS 351 (2005) 2343.

~180 E-glass fibers/LN2 tests



m = 131, 12.09%

m = 142, 6.29%

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60

ln(failure strain, %)

ln(ln(1

/1-f

))

E-glass3 C1 P1 LN

E-glass3 C2 P1 LN

E-glass3 C3 P1 LN

E-glass3 C3 P1 RH

m = 113, 12.05%

m = 117, 12.08%

20%RH, 26ºC

LN2

Fibers fail at lower strainsin ambient conditions



Fatigue effects can be characterized

RH / Temp. Sensor

Chamber purged with

controlled humidity

Failure Strain (%)

5 5.5 6 6.5 7

Cu

mu

lati

ve

Fai

lure

Pro

bab

ilit

y (

%)

1

3

5

10

20

40

60

80

90

99

4A

24oC, varied RHm

Avg = 181

Weibull Plot of 4A (0.0% B2O3)

Tested at 24 C and

different relative

humidities.

FPV = 4000 m/s

Increasing RH

80%

RH

10%

RH



Failure Strain (%)

3 4 5 6 7 8 9 10 12 14 1618

Cu

mu

lati

ve

Fai

lure

Pro

bab

ilit

y (

%)

1

3

5

10

20

40

60

80

90

99

Fresh2 days4 days7 days14 days28 days

4A Aged at

80% RH, 50oC

Tested using:

LN2, 4000 m/s

Aging effects have also been characterized

6.0

7.0

8.0

9.0

10.0

11.0

12.0

13.0

14.0

15.0

16.0

0.0 10.0 20.0 30.0 40.0 50.0

Time (Days)

Fa

ilure

Str

ain

(%

)

Aging of 4A

Aging of 4A2

Aging of 4C (set 1)

Aging of 4C (set 2)

B-free composition

Ca-aluminoborosilicates



What might inert 2pb studies tell us aboutthe failure characteristics of silicate glasses?



Compositions Studied

• xNa2O * (100-x)SiO2

• x = 0, 7, 10, 15, 20, 25, 30, 35

• xK2O * (100-x)SiO2

• x = 0, 4.5, 7, 10, 15, 20, 25

• 25Na2O * xAl2O3 * (75-x)SiO2

• x = 0, 5, 10, 15, 20, 25, 30, 32.5

• xNa2O * yCaO * (100-x-y)SiO2

– Compositions studied by Ito, et al.



Failure Strain (%)

14 15 16 17 18 19 20 21 22 23 24 25

Cu

mu

lati

ve

Fai

lure

Pro

bab

ilit

y (

%)

1

3

5

10

20

40

60

8090

99

15-85NaSi

0-100NaSi

20-80NaSi

25-75NaSi

30-70NaSi

35-75NaSi10-90

NaSi

7-93NaSi

Na-silicate inert failure strains depend on composition

Avg m ~ 259 xNa2O * (100-x)SiO2



55.0

60.0

65.0

70.0

75.0

0.00 0.10 0.20 0.30 0.40

Mole Fraction Na2O

Ela

stic M

od

ulu

s (

GP

a)

UMR

Bokin

Takahashi K.

Karapetyan

Livshits

Sodium silicate properties

15.0

17.0

19.0

21.0

23.0

25.0

0.00 0.10 0.20 0.30 0.40

Mole Fraction Na2O

Fai

lure

Str

ain

(%

)

LN4000

Increasing NBO‟s

xNa2O * (1-x)SiO2



Na-Al-silicate inert failure strains depend on composition

Failure Strain (%)

12 13 14 15 16 17 18 19 20 21 22

Cu

mu

lati

ve

Fai

lure

Pro

bab

ilit

y (

%)

1

3

5

10

20

40

60

80

90

99

25-5-70NaAlSi

25-10-65NaAlSi

25-75Na-Si

25-25-50NaAlSi

25-15-60NaAlSi

25-20-55NaAlSi

25-30-45NaAlSi

25-32.5-42.5NaAlSi

25Na2O * (x)Al2O3 * (75-x) SiO2



55.0

60.0

65.0

70.0

75.0

80.0

85.0

0.00 0.10 0.20 0.30 0.40

Mole Fraction Al2O3

Ela

stic M

odu

lus (

GP

a)

UMR

Livshits

Yoshida

13.0

14.0

15.0

16.0

17.0

18.0

19.0

20.0

21.0

0.00 0.10 0.20 0.30Mole Fraction Al2O3

Fai

lure

Str

ain (

%)

Na-Al-silicate properties depend on structure

Greater cross-linking:“stiffer” structure

Fully„cross-linked‟

0.25Na2O * (x)Al2O3

(0.75-x) SiO2



12.0

14.0

16.0

18.0

20.0

22.0

24.0

26.0

2.80 3.00 3.20 3.40 3.60 3.80 4.00

Failu

re S

train

, %

Bridging Oxygens/Former

NAS

NS

KS

SLS

Inert failure strain decreases for ‘cross-linked’ structures



Failure strain depends on elastic modulus

5.0

10.0

15.0

20.0

25.0

25.0 35.0 45.0 55.0 65.0 75.0 85.0

Elastic Modulus (GPa)

Fa

ilure

Str

ain

, %

NASNSKSNBSLSSilicaCABSTV PanelE-GlassC-0317



Do these measurements provide information about the strength of glass?

…depends on what we know aboutthe elastic modulus



Bruckner, Strength of Inorg. Glass 1986

Elastic modulus depends on strainE-glass fibers Na/Li-phosphate fibers



Strain dependence of modulus has been modeledConverting failure strain to failure stress requires knowledge of Y( ): Gupta and Kurkjian, JNCS 351 (2005) 2343

Y( ) = Y0+Y1 +(Y2/2) 2 ; f = f[(2/3)Y0+(Y1/6) f]



Failure strengths can be calculated if Y( ) is known

5.0

10.0

15.0

20.0

25.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

0.0 10.0 20.0 30.0 40.0

Iner

t Fa

ilure

Str

ain

(%

)

Mec

han

ical

Pro

per

ty (

GPa

)

mole % Na2O

stress

Pukh, et al.

strain



What role is played by ‘critical flaws’?

• There are no apparent surface heterogeneities.

• If Griffith flaws are responsible for low strengths, they will be in the range of 2-7 nm, depending on the flaw (stress concentrator) geometry.

0

2

4

6

8

10

12

14

16

0 5 10 15

Griffith Flaw Size (nm)

Fa

ilu

re S

tre

ng

th (

GP

a)

.

13GPa -> 1.4 nm flaw

6GPa -> 6.7 nm flaw

2

1

2

c

E

f

Recall processing effects



Failure Strain (%)

6 7 8 9 10 11 12 13

Cu

mu

lati

ve

Fai

lure

Pro

bab

ilit

y (

%)

1

3

5

10

20

40

60

80

90

99

Advantex C2P5

2:00 at 1180oC

m = 7

Avg = 10.36%

Advantex C2 P3

2:00 at 1250oC

m = 60

Avg = 12.11%

Advantex C2 P4

2:00 at 1200oC

m = 9

Avg = 10.88%

Advantex C2 P2

12:00 at 1350oC

m = 129

Avg = 12.18%

Advantex Failure Strains

Failure Strain (%)

4 5 6 7 8 9 10 11 12 13

Cum

ula

tive

Fai

lure

Pro

bab

ilit

y (

%)

1

3

5

10

20

40

60

80

90

99

Advantex C2 P11

3:00 at 1350oC

m = 55

Avg = 11.88%

Advantex C2 P8

0:30 at 1350oC

m = 3

Avg = 8.51%

Advantex C2 P2

12:00 at 1350oC

m = 129

Avg = 12.18%

Advantex C2 P9

1:00 at 1350oC

m = 4

Avg = 9.34%

Advantex C2 P10

2:00 at 1350oC

m = 35

Avg = 11.73%

Weibull distributions of fibers drawn after different melt histories. Weibull modulus (m),

average failure strain ( Avg), and melt history are reported for each data set.



Some questions related to Prof. Sen‟s lecture:

What type of heterogeneities might account for these

distributions in failure strains?

What techniques could you use to characterize these

heterogeneities?


IMI-87

4 .0

5 .0

6 .0

7 .0

8 .0

9 .0

1 0 .0

1 1 .0

1 2 .0

1 3 .0

0 :0 0 2 :0 0 4 :0 0 6 :0 0 8 :0 0 1 0 :0 0 1 2 :0 0 1 4 :0 0 1 6 :0 0 1 8 :0 0 2 0 :0 0 2 2 :0 0 2 4 :0 0 2 6 :0 0 2 8 :0 0

T im e

Fa

ilu

re S

tra

in,

%

1 1 0 0

1 1 5 0

1 2 0 0

1 2 5 0

1 3 0 0

1 3 5 0

Me

ltin

g T

em

pe

ratu

re (

C)

F a ilu re S tra in s

M e lt in g T e m p e ra tu re

T F ~ 1 3 5 0 ºC

T L ~ 1 2 0 0 ºC

T h e rm a l H is to ry

Im p ro v in g

D e g ra d in g

Im p ro v in g

G la s s b e h a v e s

s tra n g e ly a t T L -5 0

Advantex Thermal History Summary

Crystallites form

When the glass was melted at 1350ºC, the failure strain distributions narrow with time.

Failure strain distributions begin to broaden when melts are cooled to TL+50ºC.


How does glass break?



Inert ‘failure rate’ studies

F a ilu re S tr a in (% )

1 6 .5 1 7 1 7 .5 1 8 1 8 .5

Cu

mu

lati

ve

Fa

ilu

re P

rob

ab

ilit

y (

%)

1

3

5

1 0

2 0

4 0

6 0

8 0

9 0

9 9

In c r e a s in g Vfp

S i l ic a

mA v g

= 1 3 2

5 m /s 1 0 ,0 0 0

m /s

F a ilu re S tr a in (% )

1 6 1 6 .5 1 7 1 7 .5 1 8

Cu

mu

lati

ve

Fa

ilu

re P

rob

ab

ilit

y (

%)

1

3

5

1 0

2 0

4 0

6 0

8 0

9 0

9 9

D e c re a s in g Vfp

1 0 -1 0 -8 0

S L S

mA v g

= 1 8 9

5 m /s4 ,0 0 0 m /s

‘Normal’ Inert Fatigue

Inert Delayed Failure Effect



2.8

2.81

2.82

2.83

2.84

2.85

2.86

2.87

2.88

2.89

2.9

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0ln (Vfp)

ln (

failu

re s

train

, %

)

10-10-80 SLS

Silica

n = 1 / (d ln( / d ln(Vfp) ) n = 365

Inert ‘failure rate’ studies



The inert delayed failure effect depends on structure

-0.020

0.000

0.020

0.040

0.060

0.080

0.100

2.80 3.00 3.20 3.40 3.60 3.80 4.00

Bridging Oxygens/Former

Inert

Dela

yed F

ailu

re E

ffect

(50-

4000)/

50)

NAS

NS

KS

SLS



Failure strain measurements also correlate with crack initiation loads

13

14

15

16

17

18

19

20

21

-0.10 0.00 0.10 0.20 0.30 0.40Mole Fraction Al2O3

Fai

lure

Str

ain

(%

)

0.2

0.5

0.7

1.0

1.2

1.5

1.7

2.0

-0.10 0.00 0.10 0.20 0.30 0.40

Mole Fraction Al2O3

Cra

ck i

nit

iati

on

lo

ad (

N)

Satoshi Yoshida, 2003

0.25Na2O * (x)Al2O3 * (0.75-x) SiO2

More

Brittle



Failure strain measurements may provide information about ‘less brittle’ glasses

Setsuro Ito, 2002



2/3

4/139.2

a

CPBsBrittlenes

P is applied load, C is crack length, and a is Vickers indentation diagonal length

“Brittleness parameter” has been determined from indentation measurements

Setsuro Ito, 2002



Soda-lime silicate glasses exhibit the ‘delayed failure’ effect

Failure Strain (%)

17.5 18 18.5 19 19.5 20 20.5 21

Cu

mula

tive

Fai

lure

Pro

bab

ilit

y (

%)

1

3

5

10

20

40

60

8090

99

20-10-70SLS

mAvg

= 326

15-10-75SLS

mAvg

= 261

15-5-80SLS

mAvg

= 345

Each glass possesses a large IDFE.

Closed symbols4000 mm/sec,Open symbols

50 mm/sec



-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

4.0 5.0 6.0 7.0 8.0 9.0 10.0

Brittleness (Ito)

IDF

E (

Mis

souri S

&T

)

Silica

Soda-lime &borosilicate glasses

‘Brittleness’ and ‘inert delayed failure’may be related



Is IDFE related to network relaxation?

Day & Rindone, 1962

NBO motion?

Na diffusion



Is there a universal dependence of glass failure characteristics on network structure?

8.0

12.0

16.0

20.0

24.0

35.0 45.0 55.0 65.0 75.0 85.0 95.0 105.0

Young's modulus (GPa)

Fa

ilure

str

ain

, %

NSNASKSSLSSilicaCABSTV PanelE-glassC-0317TiMgAlSi

LN depends on E (IDFE≤0)2. Silica is anomalous

LN depends on network relaxation (IDFE>0)

WOULD ‘INSTANTANEOUS’ FAILURE STRAINS ALL FALL ON A STRAIGHT

LINE??

LN2 tests at 4000 /sec



Summary

Inert failure strains are sensitive to the composition/structure of glass fibers.

f increases when NBO’s replace BO’s

f increases when Young’s modulus decreases

Inert failure strains are dependent on the applied stressing rates (Vfp).

Structure with non-bridging oxygens fail at larger strains with slower Vfp.

‘Framework’ structures do not exhibit this ‘inert delayed failure effect’.

Is IDFE due to relaxation of the network? What role is played by the NBO’s?



The NSF/Industry/University Center for Glass Research sponsored the two-point bend studies at Missouri S&T

Nate Lower and Zhongzhi Tang collected the data

Chuck Kurkjian (retired, AT&T) inspired the work



Documents

Why Does Glass Break?